1. Technical Field
This disclosure relates to signal processing, and in particular, to sampling rates of signals.
2. Related Art
Electronic devices that communicate with one another process signals at different sampling rates. To use a signal, a device may need to convert a signal having one sampling rate into a signal having a different sampling rate. For instance, a Bluetooth headset for a cellular phone may up-sample the signal obtained from the cellular phone before the headset further processes the signal. In the context of telephony, signals are often band limited to between less than 300 Hz to 3.4 kHz, thereby severely limiting speech quality. Accordingly, pre-processing functions, such as increasing the sampling rate using interpolation, may be performed prior to an analysis done on the band limited signal in order to generate an extended bandwidth signal that supports enhanced speech quality.
Sampling rate conversion techniques, specifically up-sampling techniques, may use interpolation, such as Lagrange interpolation and cubic splines polynomial fitting. Other systems may convert between sampling rates by highly over-sampling a signal and choosing the closest artificially generated time sample. In these systems, the higher the over-sampling rate, the lower the corresponding error is, Some systems may use a quasi-continuous interpolation of individual samples x(n) of a continuous absolutely integrable signal x(t), employing the sinc function, to generate a signal value at the desired sampling time Ta, as follows:
                    x        ⁡                  (                      T            a                    )                    =                        ∑                      n            =                          -              ∞                                ∞                ⁢                              x            ⁡                          (              n              )                                ⁢                                    h              s                        ⁡                          (                                                T                  a                                -                                  nT                  in                                            )                                            ,                  ⁢    with                                h          s                ⁡                  (          t          )                    =                        sin          ⁢                                          ⁢                      c            ⁡                          (                                                f                  in                                ⁢                t                            )                                      :=                              sin            ⁡                          (                              π                ⁢                                                                  ⁢                                  f                  in                                ⁢                t                            )                                            π            ⁢                                                  ⁢                          f              in                        ⁢            t                                ,  with Tin denoting the input sampling period, and fin denoting the input sampling rate.
These systems and methods may require a large amount of resources. Some systems may need a long computing time to perform calculations. Other systems may require a large amount of memory to store sample information. Thus, sampling rate conversion remains a significant problem in modem signal processing systems and in modem devices that often have severely limited processing capability, memory resources, and power reserves.
Therefore, a need exists for an improved sampling rate conversion system.